Last Saturday, around fifty activists crammed into one of the University of London Union's third-floor rooms to discuss the Respect campaign for the Greater London Assembly elections. The size of the meeting, and the geographical breadth it represented, came as a very pleasant surprise to many. Branches had sent on or two delegates each, which meant that the meeting represented a large and geographically diverse range of branches. Even areas where we are relatively weak, like south-east London, had some representation. Despite the internal arguments of the last few months, Respect activists across London were prepared to throw themselves into the campaign.

Because the possibilities remain: from the incipient recession, to the continuing occupation of Iraq , the space for a non-Labour left has expanded as perhaps never before. One important indicator is that those representing Old Labour values and significant social forces, previously tied exclusively to Labour, have seen where Brown is taking the Party, and have started to look elsewhere – not necessarily to Respect, naturally, but outside of Labour's thinning ranks.

So the large turnout was important. This was pretty much the first chance for Respect activists to meet up since "Respect Renewal" split from the organisation, and the first that provided the opportunity for a serious discussion of our strategy. George Galloway's exit from Respect had proved a distraction from real political work.

Discussion centred on two main points: first, a broad look at our strategy in the campaign; second, getting down to the hard slog of building an organisation and campaigning on the ground. The London elections are complex, by British standards: there's a mayor and a GLA to vote for. Each uses a somewhat different electoral system: you cast a first preference and a second preference for mayor, but you vote for a constituency candidate and then a party list for the GLA.

The party list vote is used to ensure the proportion of seats on the GLA matches parties' proportions of the citywide vote, and so smaller parties can manage to get a seat with a good poll across London. And – importantly – the preference system in the mayoral vote means you can vote for the candidate you actually like, followed by the candidate that will keep the Tories out – current mayor, Ken Livingstone. As he said, back in 2004, calling for a second preference Livingstone vote allowed Lindsey German and Respect to "campaign for her political position without risking a Tory victory."

This matters, because Livingstone's posse have been putting the word out that a left-wing challenge to the incumbent mayor will let the Conservatives take power in London. Either they don't understand the voting system or, more likely, they are being totally disingenuous: standing in the mayoral contest provides a brilliant platform for a candidate, with invites to hustings, media interviews, and so on, as well as London-wide mailshot of the candidate's manifesto. You don't get any of this if you just stand for the Greater London Assembly – a credible campaign for the GLA, in other words, absolutely demands that you also stand a candidate for mayor.

If you're pessimistic about building a non-Labour left, or simply wedded to the Labour Party, a credible campaign by the non-Labour left is the last thing you want to see. But Livingstone needs a left-wing challenge. His combination of nice noises about the war with appeasement for the City of London deserves to meet some opposition from the Left. It's absurd that Livingstone's (correct and necessary) opposition to Islamophobia should be taken as the only test he needs to pass; actually, this is the minimum we should be expecting from the "socialist" mayor of one of the most unequal cities in Europe. We simply have to raise our sights, and start to challenge the revolting concentrations of wealth, power and privilege that exist in London and across the UK.

Respect is unique in being the only electable organisation standing in these elections with anything worthwhile to say about the economy and, in particular, the City. No-one else will touch the bankers and the speculators: Livingstone has bent over backwards to accomodate them for the last eight years; Johnson doubtless fagged for a few at Eton; and the Lib Dems are firmly committed to the City's agenda, proposing (amongst other things) to ban strikes for public sector workers. Even the Green Party in London , as far as can be told, has said nothing on the issue.

So on what is fast becoming the most decisive political question – and the economy is a political question, whatever our neoliberal friends say – the main parties are in consensus: no challenge to the City, no change to the status quo.

This is hugely to Respect's advantage. There's a crying need for someone to stand up to the sort of free-market vanishing-point lunacy that has just seen the Government desperately bribing fat cats with our money to take Northern Rock off its hands. Livingstone and the London Labour Party aren't going to.

Of course, the recent attacks on Livingstone have been unfair: in many ways, I can't think of a better Mayor for the City, one better able to soft-soap his left-leaning constituents into accepting a London Plan written fundamentally entirely around the City's needs, or into tolerating a chief economic advisor (John Ross) who sings the praises of hedge funds. Former Tory candidate Stephen Norris couldn't do it: much of London would be up in arms if this king of PFI tried anything similar. Likewise for Johnson. That Livingstone's vision for the capital has effectively collapsed into City boosterism is a terrible shame – it's not particularly surprising since he's pulled, especially, by his ties to New Labour - but it is still a shame.

As such, there's an air of unreality about the politically unhinged Martin Bright laying into Livingstone for being too left-wing. It goes without saying that Livingstone needs defending from the red-baiting filth Bright and his new Tory friends are hawking about: Bright, this professional Islam-basher and habitual friend of the hard Right, should be treated with the contempt he richly deserves. It should go without saying, too, that Livingstone deserves any left-winger's second preference – better a London mayor who opposes the Iraq war and racism, than a racist who militantly supported the invasion of Iraq. It's perfectly obvious which one is closer to ordinary Londoners.

There's an argument out there that the Left shouldn't even stand against Livingstone for precisely those reasons. It was kind of "Respect Renewal" to confirm everything we said about their split from Respect by having their leadership come out in wholehearted support of Labour's candidate for Mayor. It's perfectly clear, now, that what took place was a left-right split: one side wanted an independent, non-Labour organisation of the Left; the other side was quite prepared to compromise with New Labour, even to the point of ducking key political questions. And the outbreaks of bafflement and consternation amongst the waifs and strays on what we must suppose is Renewal's left-wing show exactly why a new formation of the Left needs a leadership accountable to its members – which was, of course, precisely the point.

Although I strongly suspect those elements of Renewal's leadership now trooping off rightwards to a happy marriage with New Labour would dearly love to really trash Respect on the way, they're not in a good position to do so: they've ruled out a mayoral candidate and they're only standing one constituency candidate in the GLA. However, they've put the word out that George Galloway will be heading up an anti-Respect GLA slate.

This may just be an attempt to put the frighteners on Respect, because it looks distinctly cack-handed otherwise: aside from the lopsidedness of supporting Livingstone, but then opposing his party, I will be amazed if they can mobilise the sort of London-wide political resources they need to run a convincing campaign across the city – especially without the added publicity of a mayoral candidate. One of the perils of relying too heavily on local opportunism is that you end up with the bulk of your membership scarcely bothered by what happens on the other side of Whitechapel High Street, let alone Norwood or Uxbridge.

Last April, when Lindsey German was selected unanimously by a meeting of more than 300 Respect members, the arguments were very different. Responding to a Morning Star editorial, which opposed a Respect mayoral bid, George Galloway MP and Lindsey German wrote a 900 word reply, which the Morning Star reprinted. They expressed surprise that the Star would urge a "free run" for Livingstone. "The Respect candidate came fifth in the last election, beating both the British National Party and the Greens. Yet you do not direct your appeal to the Green Party, which could also be accused of splitting the vote." Further:

The electoral system for London mayor actually makes it very hard for the vote to be split, since it operates on the basis of transfers - all candidates bar the top two have their second preference vote distributed to eventually determine the winner. Respect's candidate was the only one to call clearly for transfers to Ken in 2004 and more than a quarter of those voters responded - a relatively high proportion. And there is no reason to suppose that, if Respect does not stand, its voters will turn out in a greater proportion than our transfers and vote for Ken.

They stressed the importance of a "strong left voice" being expressed on "the issues facing Londoners - the acute housing crisis, which is not being dealt with, the transport system, which is both the most expensive and one of the worst in the world, the privatisation of the East London Line and the business agenda, which is making London a worse place for many of the poor to live". And they added:

Many Londoners are dissatisfied with the record of new Labour in government and will not turn out to vote Labour in the numbers that they once did. A vote for Respect by these people will help the left and can help Ken by lifting the left vote overall from people who might otherwise abstain.

A good vote for Respect will also help to keep the fascist BNP off the assembly. More votes for new Labour will not keep the BNP off the assembly, because the proportional representation system favours the election of smaller parties. So, the only way of keeping the BNP off is to vote for a left-wing, smaller party.

Respect is the obvious candidate for this vote - but its chances will be undermined without the publicity that comes from standing a mayoral candidate.

These arguments are as incisive today as they were in April. The difference is that George Galloway and his supporters are no longer making them. No matter. Respect, as the GLA meeting showed, has activists in place from Newham to Neasden. Reports across the city are promising: Respect members are involved in campaigns to defend victimised trade unionists, against council house stock transfer, and against city academies. In Waltham Forest, north-east London, we face an immediate electoral challenge with a local council by-election. There are very good reason to think we can get a credible vote. There's no guarantee about this, especially with Labour and the Lib Dems throwing themselves into the contest, but if our candidate, Carole Vincent, can get the sort of vote Respect has been achieving up and down the country, we'll be on target for the GLA. (Anybody wanting to help with the campaign can find details here.)

Around 23% of our vote came from the City and East constituency, where Galloway currently has his only activist base. Even if half of that vote disappears as a result of the split, a good campaign across the rest of London still puts the GLA well within our grasp. There is not only a need but a real thirst for a left-wing challenge to the neoliberal consensus. It can be seen all over: from the sold-out film-showing we held last Sunday, to the excellent recent attendances for Respect meetings across the country.

We've also had vastly more experience running elections now, and have a hugely higher brand recognition, and a significantly larger membership and activist base. The split has damaged us, of course, but not as much as might be supposed: and, remember, we elected our first councillor a long time before we elected George Galloway. It was impossible to come away from the GLA planning meeting without thinking that we were in with a shout, giving a voice to the hundreds of thousands of ordinary, working-class Londoners excluded by all the main parties.

The Respect GLA campaign launch is a week today, Thursday, 31 January, at Conway Hall, Red Lion Square WC1, from 7.30pm. If you want an alternative in London to the parties of neoliberalism and war, you need to be there.